malachite_float/comparison/
partial_cmp_abs_primitive_int.rs

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
// Copyright © 2025 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.

use crate::Float;
use crate::InnerFloat::{Finite, Infinity, NaN, Zero};
use core::cmp::Ordering::{self, *};
use malachite_base::num::arithmetic::traits::UnsignedAbs;
use malachite_base::num::basic::signeds::PrimitiveSigned;
use malachite_base::num::basic::unsigneds::PrimitiveUnsigned;
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_nz::natural::Natural;

fn float_partial_cmp_abs_unsigned<T: PrimitiveUnsigned>(x: &Float, y: &T) -> Option<Ordering>
where
    Natural: From<T>,
{
    match (x, y) {
        (float_nan!(), _) => None,
        (Float(Infinity { .. }), _) => Some(Greater),
        (float_either_zero!(), y) => Some(if *y == T::ZERO { Equal } else { Less }),
        (
            Float(Finite {
                exponent: e_x,
                significand: sig_x,
                ..
            }),
            y,
        ) => Some(if *y == T::ZERO {
            Greater
        } else if *e_x <= 0 {
            Less
        } else {
            u64::from(e_x.unsigned_abs())
                .cmp(&y.significant_bits())
                .then_with(|| sig_x.cmp_normalized(&Natural::from(*y)))
        }),
    }
}

macro_rules! impl_from_unsigned {
    ($t: ident) => {
        impl PartialOrdAbs<$t> for Float {
            /// Compares the absolute values of a [`Float`] and an unsigned primitive integer.
            ///
            /// NaN is not comparable to any primitive integer. $\infty$ and $-\infty$ are greater
            /// in absolute value than any primitive integer. Both the [`Float`] zero and the
            /// [`Float`] negative zero are equal to the integer zero.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
            ///
            /// # Examples
            /// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
            #[inline]
            fn partial_cmp_abs(&self, other: &$t) -> Option<Ordering> {
                float_partial_cmp_abs_unsigned(self, other)
            }
        }

        impl PartialOrdAbs<Float> for $t {
            /// Compares the absolute values of an unsigned primitive integer and a [`Float`].
            ///
            /// No primitive integer is comparable to NaN. Every primitive integer is smaller in
            /// absolute value than $\infty$ and $-\infty$. The integer zero is equal to both the
            /// [`Float`] zero and the [`Float`] negative zero.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `other.significant_bits()`.
            ///
            /// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
            #[inline]
            fn partial_cmp_abs(&self, other: &Float) -> Option<Ordering> {
                other.partial_cmp_abs(self).map(Ordering::reverse)
            }
        }
    };
}
apply_to_unsigneds!(impl_from_unsigned);

fn float_partial_cmp_abs_signed<T: PrimitiveSigned>(x: &Float, y: &T) -> Option<Ordering>
where
    Natural: From<<T as UnsignedAbs>::Output>,
{
    match (x, y) {
        (float_nan!(), _) => None,
        (Float(Infinity { .. }), _) => Some(Greater),
        (float_either_zero!(), y) => Some(if *y == T::ZERO { Equal } else { Less }),
        (
            Float(Finite {
                exponent: e_x,
                significand: sig_x,
                ..
            }),
            y,
        ) => Some(if *y == T::ZERO {
            Greater
        } else if *e_x <= 0 {
            Less
        } else {
            u64::from(e_x.unsigned_abs())
                .cmp(&y.significant_bits())
                .then_with(|| sig_x.cmp_normalized(&Natural::from(y.unsigned_abs())))
        }),
    }
}

macro_rules! impl_from_signed {
    ($t: ident) => {
        impl PartialOrdAbs<$t> for Float {
            /// Compares the absolute values of a [`Float`] and a signed primitive integer.
            ///
            /// NaN is not comparable to any primitive integer. $\infty$ and $-\infty$ are greater
            /// in absolute value than any primitive integer. Both the [`Float`] zero and the
            /// [`Float`] negative zero are equal to the integer zero.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
            ///
            /// # Examples
            /// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
            #[inline]
            fn partial_cmp_abs(&self, other: &$t) -> Option<Ordering> {
                float_partial_cmp_abs_signed(self, other)
            }
        }

        impl PartialOrdAbs<Float> for $t {
            /// Compares the absolute values of a signed primitive integer and a [`Float`].
            ///
            /// No primitive integer is comparable to NaN. Every primitive integer is smaller in
            /// absolute value than $\infty$ and $-\infty$. The integer zero is equal to both the
            /// [`Float`] zero and the [`Float`] negative zero.
            ///
            /// # Worst-case complexity
            /// $T(n) = O(n)$
            ///
            /// $M(n) = O(1)$
            ///
            /// where $T$ is time, $M$ is additional memory, and $n$ is `other.significant_bits()`.
            ///
            /// See [here](super::partial_cmp_abs_primitive_int#partial_cmp_abs).
            #[inline]
            fn partial_cmp_abs(&self, other: &Float) -> Option<Ordering> {
                other.partial_cmp_abs(self).map(Ordering::reverse)
            }
        }
    };
}
apply_to_signeds!(impl_from_signed);